Title: QUADRATIC FUNCTIONS Author: San Juan College Last modified by: rabuckv Created Date: 5/28/1995 4:29:18 PM Document presentation format: On-screen Show
No vertical asymptotes H.A.: y = 3 Guided Practice Find the horizontal and vertical asymptotes of the given function. Use limits to describe the corresponding behavior.
If the numerator is a larger degree than the denominator The equation of the asymptote ... Step One: Find the domain of the rational function ... Rational Functions ...
Horizontal asymptote: y = 2. Check Graph the function on a ... x = 1. As a result, the graph of the function has a vertical asymptote at the line x = 1. ...
Rational Functions Rational Functions ... of each term and not the variables Example Practice Multiplying/Dividing ... still apply when working with rational expressions!
Let's Translate. Recall what happens to the graph of a function when we ... Translate ... Page 615: 1, 3, 8, 12 (Make sketches now, no graph paper needed until HW) ...
section 3.2 rational functions rational functions rational functions take on the form: examples: domain of rational functions any value which zeros out the ...
On June 4 1996 the first flight. of the ... Banking bugs. Software bugs caused the bank accounts of 823customers of a ... have bugs? Programming errors ...
Determine the vertical asymptotes (if any) of a rational function. ... vertical asymptotes, and horizontal asymptotes for ... Find the slant asymptote for ...
quotient of two polynomials is called a rational expression. ... shows up as an asymptote. An. asymptote is a line that a. curve approaches but never ...
UNIT 4: rational functions 8-3 Graphing Rational functions Rational Functions Define Rational Function: is a function with two polynomials (one in the numerator ...
Graphing Rational Functions Graph the Rational Function Step II: Graph using the information you found in Step I Ex 1. Graph the Rational Function Step II: Graph ...
Graphing General Rational Functions p. 547 Steps to graphing rational functions Find the y-intercept. ... State domain & range. 2. x-intercepts: x=0 3.
Polynomial and Rational Functions Chapter 3 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAA Quadratic Functions and Models ...
8.2 Graph Simple Rational Functions Rational Function A function of the form where p(x) & q(x) are polynomials and q(x) 0. Hyperbola A type of rational function.
We want to graph this rational function showing all relevant characteristics. ... Numerator: Factor out a GCF of x2. Denominator: Factor as a perfect square trinomial. ...
9.3 Graphing General Rational Functions p. 547 Steps to graphing rational functions Find the y-intercept. Find the x-intercepts. Find vertical asymptote(s).
Lesson 2-7: Graphing Rational Functions Advanced Math Topics Definitions Continuity: a graph that is able to be traced without picking up the pencil Asymptote: a line ...
Unit 4 Rational functions 8-6 Solving rational expressions Solving Rational Equations To solve a rational equation first multiply each side by the LCD.
slant asymptotes degree of denom is 1 or higher & numerator is exactly 1 more ... otherwise it's a vertical asymptote. Look at degree of num & denom. ...
Here I only plotted one more point at x=2 since a point hadn't been plotted to ... For the section between the V.A.'s, we use that it can't cross the H.A. ...
Hence, there are no intersections between the graph of f(x) and the H.A. ... Here I only plotted one more point at x=-1 since a point hadn't been plotted to ...
If the y values approach a real number b, then b is the horizontal asymptote. ... The quotient from long division will give the equation for the oblique asymptote. ...
7. Graph the function on the calculator. 8. Use the results above to graph the equation by hand. ... Simplify the terms and then factor. Draw a number line. ...
Chapter 6 Rational Expressions, Functions, and Equations 6.1 Rational Expressions and Functions: Multiplying and Dividing Blitzer, Intermediate Algebra, 5e ...
Rational functions: Distance, rate, and time Consider the function t(r) = time required to cover distance of 300 miles at a rate of r mph As rate increases, time ...
Right of vert. asymp. Example 3. Graph. State domain & range. Vertical asymptote: ... Vert asymp: x 2 = 0. x = 2. 3. x y -1 0. 0 2. 1 6. 3 -4. 4 0. Left of x ...
... we see that there is a vertical asymptote at x = 2 because the graph approaches ... see that y = 0 is a horizontal asymptote of the function since y tends to go ...
Title: Radical Functions and Rational Exponents Author: MSHS Last modified by: HP Authorized Customer Created Date: 8/10/2004 8:30:57 PM Document presentation format
Sullivan Algebra and Trigonometry: Section 4.3 Rational Functions I Objectives Find the Domain of a Rational Function Determine the Vertical Asymptotes of a Rational ...
Any values of x that are not in the domain of the function but are not V.A. ... of the hole, plug 0 into the reduced form. Graphing Rational Functions ...
Rational Functions/Restricted Values. What do we notice? The graph has two branches. Because no point of the graph ... The line is called a VERTICAL ASYMPTOTE. ...
9.2 Graphing Simple Rational Functions (p. 540) Rational Function A function of the form where p(x) & q(x) are polynomials and q(x) 0. Hyperbola A type of rational ...
Polynomial, Power, and Rational Functions. Chapter 2. Linear and ... Superimpose the graph of the regression model on the scatter plot, and observe the fit. ...
Chapter 4 Polynomials and Rational Functions 4.1 Polynomial Functions Def: A polynomial in one variable, x, is an expression of the form . The coefficients a0 ...
Since the domain is , and the vertical asymptotes are x = 2, -1, that means that ... Horizontal asymptotes describe the behavior at the ends of a function. ...
... Asymptote ... all holes and vertical asymptotes in each graph. Horizontal Asymptote ... Identify all excluded values, asymptotes, and holes in. the graph of a ...
How to sketch graphs of rational functions that have slant asymptotes ... Asymptotes. Vertical. at zeros of the denominator. Horizontal. N D asymptote at y = 0 ...